New biconvex optimization for planning of battery energy storage systems

Battery energy storage systems (BESS) are increasingly crucial in balancing electricity production and consumption in modern power grids, due to their decreasing capital cost, flexibility, and short response time. However, existing BESS optimization models often have complex, non-linear, and non-convex objectives and constraints. We recently proposed a voltage-current arbitrage model (VIAM) for BESS control using a linear approximation of the open circuit voltage and battery status dependency function. This model, called the linearly constrained exponential optimization model, has an effective algorithm, but it's unclear if its solutions are globally optimal. Moreover, using a linearized function in the VIAM can lead to profit loss. This paper presents a new reformulation of the VIAM as a biconvex optimization problem, which can be reduced to convex optimization under certain conditions, allowing for effective location of global optimal solutions. We also propose a new approximation scheme for the original non-linear function using piece-wise linear and quadratic functions, leading to a quadratically constrained biconvex optimization model. We developed a novel sequential dynamic linear/quadratic approximation algorithm for this model and conducted preliminary experiments to demonstrate its efficacy and efficiency.